1)
48 = 2⁴ · 3
64 = 2⁶
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[48, 64] = 2⁶· 3 = 192
(48, 64) = 2⁴ = 16
2)
[tex]\it a)\ \dfrac{20}{x}=\dfrac{180}{63} \Rightarrow x = \dfrac{20\cdot63}{180} =7\\ \\ \\ b)\ \\ \\ 10m ---------- 12z\\ 15m ----------\ xz[/tex]
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Avem proporționalitate inversă, deci:
[tex]\it \dfrac{10}{15} = \dfrac{x}{12} \Rightarrow x=\dfrac{10\cdot12}{15} = 8\ zile[/tex]
3)
[tex]\it 36\%\ din\ 150=\dfrac{36}{100}\cdot150=54[/tex]
4)
[tex]\it a)\ =\dfrac{4}{9}\cdot\Big(\dfrac{3}{9}+\dfrac{1}{2}\cdot\dfrac{4}{3}\Big)\cdot\dfrac{9}{8}=\dfrac{4}{9}\cdot\dfrac{9}{8}\Big(\dfrac{1}{3}+\dfrac{2}{3}\Big)=\dfrac{1}{2}\cdot\dfrac{3}{3}=\dfrac{1}{2}\cdot1=\dfrac{1}{2}[/tex]
[tex]\it b)\ =-169:(-8-12+7) =-169:(-13)=13[/tex]
5)
[tex]\it \dfrac{6}{2x+1}\in\mathbb{Z} \Rightarrow 2x+1\in D_6\ \ \ \ (1)\\ \\ \\ x\in\mathbb{Z} \Rightarrow 2x+1=impar\ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow 2x+1\in\{-3,\ -1,\ 1,\ 3\}|_{-1} \Rightarrow 2x\in\{-4,\ -2,\ 0,\ 2\}|_{:2}\Rightarrow\\ \\ \Rightarrow x\in\{-2,\ -1,\ 0,\ 1\}[/tex]
